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Let's say we have an equation in n variables of the form, $y=(a_1x_1+a_2x_2+.....a_{n-1}x_{n-1}+c) \ mod\ k$. We are interested in finding the coefficients $a_i$'s. Given a set of say N points, we can generate N equations in modular arithmetic. Here k is a power of 2 so approaches involving prime numbers don't apply here. Also the application I have involves a bound on the value of each coefficient say M. Is there any algorithm to solve this? Some approaches involving a variant of Gaussian elimination have been discussed but the approach isn't clear.

Thanks in advance!

Anmol Mahajan
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  • See e.g. here: https://math.stackexchange.com/q/2556129/86776 – mvw May 29 '18 at 11:29
  • What are the limitations of this approach? Especially given k is not a prime. I'm not too clear with how to deal with the case when inverse doesn't exist. Could you point me to some relevant theory? Or any generalizations for solving Gaussian elimination in modular arithmetic?

    I've been following this link - https://math.stackexchange.com/questions/1565792/how-do-you-solve-a-system-of-linear-equations-in-modular-arithmetic

     – Anmol Mahajan Jun 01 '18 at 08:16

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